A059802 -id:A059802 - cp's OEIS frontend

A062573 Numbers k such that 7^k - 6^k is prime.

2, 3, 7, 29, 41, 67, 1327, 1399, 2027, 69371, 86689, 355039

Offset: 1

Mike Oakes, May 18 2001, May 19 2001

Terms greater than 1000 often correspond only to strong probable primes.

			7^2 - 6^2 = 49 - 36 = 13, which is prime, so 2 is in the sequence.
7^3 - 6^3 = 343 - 216 = 127, which is prime, so 3 is in the sequence.

Henri & Renaud Lifchitz, Top probable primes of the form 7^p-6^p

Cf. A000043, A057468, A059801, A059802, A062572-A062666.

Select[Range[100], PrimeQ[7^# - 6^#] &] (* Alonso del Arte, Sep 04 2013 *)

is(n)=ispseudoprime(7^n-6^n) \\ Charles R Greathouse IV, Feb 20 2017

Two more terms (69371 and 86689) found by Predrag Minovic in 2004 corresponding to probable primes with 58626 and 73261 digits. - Jean-Louis Charton, Oct 06 2010

New term 355039 found by Jean-Louis Charton in May 2011 corresponding to a probable prime with 300043 digits.

A062574 Numbers k such that 8^k - 7^k is prime or a strong pseudoprime.

Original entry on oeis.org

7, 11, 17, 29, 31, 79, 113, 131, 139, 4357, 44029, 76213, 83663, 173687, 336419, 615997

Offset: 1

Mike Oakes, May 18 2001, May 19 2001

All terms are prime. - Alexander Adamchuk, Apr 27 2008

Henri & Renaud Lifchitz, PRP Records.

Cf. A000043, A057468, A059801, A059802, A059803 (9^n-8^n is prime), A062572-A062666.

Cf. A016177 = 8^n - 7^n.

Select[Range[200], PrimeQ[8^# - 7^#] &] (* Vladimir Joseph Stephan Orlovsky, Feb 22 2012 *)

is(n)=ispseudoprime(8^n-7^n) \\ Charles R Greathouse IV, Sep 04 2013

Two more terms 44029 and 76213 found by Ananda Tallur & Jean-Louis Charton in 2003.
Three more terms 83663, 173687 and 336419 found by Jean-Louis Charton in 2004 and 2008
New term 615997 found by Jean-Louis Charton corresponding to a probable prime with 556301 digits. Jean-Louis Charton, Sep 02 2009

A062585 Numbers k such that 19^k - 18^k is prime.

Original entry on oeis.org

2, 1607, 1873, 10957

Offset: 1

Mike Oakes, May 18 2001, May 19 2001

PrimePi[ a(n) ] = {2, 253, 287, 1331, ...}. - Alexander Adamchuk, Feb 16 2007
a(5) > 10^5. - Robert Price, Jun 05 2012
Terms greater than 1000 may correspond to (unproven) strong pseudoprimes. - M. F. Hasler, Sep 16 2013

Cf. A000043, A057468, A059801, A059802, A062572-A062583, A188051, A062586-A062666.

is(n)=ispseudoprime(19^n-18^n) \\ Charles R Greathouse IV, Feb 20 2017

10957 (found by Mike Oakes in 2003) from Alexander Adamchuk, Feb 16 2007

A062592 Numbers k such that 26^k - 25^k is prime or a strong pseudoprime.

Original entry on oeis.org

3, 7, 97, 109, 401, 431

Offset: 1

Mike Oakes, May 18 2001, May 19 2001

a(7) > 10^5. - Robert Price, Nov 10 2012

Cf. A000043, A057468, A059801, A059802, A062572-A062589, A214658, A214655, A062593-A062666.

Edited by M. F. Hasler, Sep 21 2013

A121091 Smallest nexus prime of the form n^p - (n-1)^p, where p is an odd prime.

Original entry on oeis.org

7, 19, 37, 61, 4651, 127, 1273609, 2685817, 271, 331, 397, 6431804812640900941, 547, 631, 5613125740675652943160572913465695837595324940170321, 371281, 919

Offset: 2

Alexander Adamchuk, Aug 11 2006, revised Dec 01 2006, Feb 15 2007

nonn

a(19) = 19^1607 - 18^1607, which is too large to include. It has 2055 decimal digits. See A062585(1) = 1607.

a(20)-a(21) = {723901, 8005616640331026125580781}. a(n) is currently known for all n up to n = 96. Corresponding smallest odd primes p such that (n+1)^p - n^p is prime are listed in A125713(n) = {3,3,3,3,5,3,7,7,3,3,3,17,3,3,43,5,3,10957,5,19,127,229,3,3,3,13,3,3,149,3,5,3,23,3,5,83,3,3,37,7,3,3,37,5,3,5,58543,...}. a(n+1) = A065013(n) for n = {4, 7, 10, 12, 13, 16, 17, 19, 22, 24, 25, 27, 28, 31, ...} = A047845(n) = (n-1)/2, where n runs through odd nonprimes (A014076), for n>1.

Cf. A121620, A000043, A058765, A121616, A121618.
Cf. A125713 = Smallest odd prime p such that (n+1)^p - n^p is prime. Cf. A065913 = Smallest prime of form (n+1)^k - n^k. Cf. A058013 = Smallest prime p such that (n+1)^p - n^p is prime. Cf. A047845, A014076.
Cf. A062585 = numbers n such that k^n - (k-1)^n is prime, where k is 19. Cf. A000043, A057468, A059801, A059802, A062572-A062666.

a(n) = n^A125713(n) - (n-1)^A125713(n).

A214655 Numbers n such that 25^n - 24^n is prime or a strong pseudoprime.

Original entry on oeis.org

3, 5, 29, 54799

Offset: 1

Robert Price, Jul 24 2012

All terms are prime.

No other terms less than 10^5. - Robert Price, Jul 24 2012

Cf. A000043, A057468, A059801, A059802, A059803, A062572-A062589, A214658, A062592-A062666.

Select[Range[10^5], PrimeQ[25^#-24^# ]&]

Edited by M. F. Hasler, Sep 21 2013

A214658 Numbers n such that 24^n - 23^n is prime or a strong pseudoprime.

Original entry on oeis.org

2, 3, 31, 40519, 51061

Offset: 1

Robert Price, Jul 24 2012

All terms are prime.

No other terms less than 10^5. - Robert Price, Jul 24 2012

Cf. A000043, A057468, A059801, A059802, A059803, A062572-A062589, A214655, A062592-A062666.

Select[Range[10^5], PrimeQ[24^#-23^# ]&]

A062578 Numbers k such that 12^k - 11^k is prime.

Original entry on oeis.org

2, 3, 7, 89, 101, 293, 4463, 70067

Offset: 1

Mike Oakes, May 18 2001, May 19 2001

Terms greater than 1000 may correspond to unproven strong pseudoprimes.

Cf. A000043, A057468, A059801, A059802, A062572-A062666.

is(n)=ispseudoprime(12^n-11^n) \\ Charles R Greathouse IV, May 22 2017

New term 70067 (found in 2006) from Jean-Louis Charton, Sep 02 2009

Edited by M. F. Hasler, Sep 16 2013

A147667 Primes of the form 5^k - 4^k.

Original entry on oeis.org

61, 1136791005963704961126617632861, 173472015290681763212224222187425603741981, 31861838222649045530727106406255616308752331078816472270207782250106896363274089867800367051529351065966102374800998198276889145001421

Offset: 1

Vladimir Joseph Stephan Orlovsky, Nov 10 2008

nonn

All terms are odd, and if k is even, then 5^k - 4^k is divisible by 3. [Vincenzo Librandi, Nov 25 2010]

The next term (a(5)) has 156 digits. - Harvey P. Dale, May 14 2022

			5^3 - 4^3 = 125 - 64 = 61.

Muniru A Asiru, Table of n, a(n) for n = 1..9

Cf. A059802 (corresponding n).

Filtered(List([1..200],n->5^n - 4^n),IsPrime); # Muniru A Asiru, Mar 04 2018

select(isprime, [seq(5^n - 4^n, n=0..200)]); # Muniru A Asiru, Mar 04 2018

lst={};Do[p=5^n-4^n;If[PrimeQ[p],AppendTo[lst,p]],{n,6!}];lst
Select[Table[5^n-4^n,{n,300}],PrimeQ] (* Harvey P. Dale, May 14 2022 *)

A188051 Numbers k such that 18^k - 17^k is prime, or a strong pseudoprime.

Original entry on oeis.org

3, 13, 71, 14533, 26641, 48179

Offset: 1

Jean-Louis Charton, Mar 19 2011

Terms < 10000 found by Mike Oakes.
Term 14533 found by Lelio R Paula in June 2008 corresponding to a probable prime with 18243 digits.
Terms 26641 and 48179 found by Jean-Louis Charton in December 2010 corresponding to probable primes with 33442 and 60478 digits.
a(7) > 10^5. - Robert Price, Nov 30 2012

Top probable primes of the form 18^p-17^p

Cf. A000043, A057468, A059801, A059802, A059803, A062572-A062583, A062585-A062666.

is(n)=ispseudoprime(18^n-17^n) \\ Charles R Greathouse IV, Jun 06 2017

Edited by M. F. Hasler, Sep 21 2013

cp's OEIS Frontend

A062573 Numbers k such that 7^k - 6^k is prime.

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A062574 Numbers k such that 8^k - 7^k is prime or a strong pseudoprime.

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A062585 Numbers k such that 19^k - 18^k is prime.

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A062592 Numbers k such that 26^k - 25^k is prime or a strong pseudoprime.

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A121091 Smallest nexus prime of the form n^p - (n-1)^p, where p is an odd prime.

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A214655 Numbers n such that 25^n - 24^n is prime or a strong pseudoprime.

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A214658 Numbers n such that 24^n - 23^n is prime or a strong pseudoprime.

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A062578 Numbers k such that 12^k - 11^k is prime.

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A147667 Primes of the form 5^k - 4^k.

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